Hi, I'm in a slightly awkward situation because I have very few professors to ask for letters of rec. Here's my story:
I went to college A for 1 year, then transferred to college B. College A is ranked low for math. College B is a top 10 school for math, but because I transferred with a lot of credits, I am expected to graduate in 2 years. So I'm only spending 3 years total in college. I am graduating next year, and applying for grad school this fall.
Here are some Professors I can potentially ask for letters of Rec:
Professor W- during the summer between college A and before starting school in college B, I did an REU at a low ranked college (75th-100th). I did well in the REU, and I wrote a joint paper in combinatorics. But I'm not interested in that field, and the research wasn't very high quality. However, I know that Prof W would write me a strong letter of rec.
Professor X- he's a prof at college B, and is well known in his field. I did a reading course with him (along with some grad students), but I personally felt that the course was going too quickly for me and I did not understand much of what was going on. The way the course worked was that one person gives a talk each week explaining whatever topic we were studying. I did one talk, which (luckily) was relatively easier than the other topics people were covering. Basically, I don't feel like I was as involved in the course as I should have, so I'm not sure what Prof X would write if I asked him for a letter.
Professor Y-he's also a prof at college B, and is well known. I'm technically doing a reading course with him this summer, but since he is really busy I'm actually doing a reading course with a grad student. Should I ask the grad student to write something about me to give to Prof Y, and ask Prof Y to write me a letter of rec?
Professor Z-he's also a prof at college B, but he is younger (assistant prof). I took two (graduate) classes with him, and although he gave me A's, his grading method is pretty lax, and I feel like I don't know as much as I should. I feel stupid around him because when he lectures, he talks as if we are familiar with the topic. The courses I took with him had very difficult material and even now I do not feel confident about it. I am thinking of doing a reading course with him this fall however. I did not ask him yet. If I ask him for a letter of rec, I don't know what he will say. I feel it will be lukewarm.
So the question is, who should I ask? I was originally thinking X,Y,Z, but then I feel like all my recommendations will be lukewarm at best. I would ask W, but he's from a lesser ranked college so im not sure...